In how many ways can the letters of the word INDIA be permutated such that in each combination, vowels should occupy odd positions?

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NDA-II 2024 (Maths) Official Paper (Held On: 01 Sept, 2024)
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  1. 3
  2. 6
  3. 9
  4. 12

Answer (Detailed Solution Below)

Option 2 : 6
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Detailed Solution

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Explanation:

Word 'INDIA' contains three vowels (I, I and A) and two consonants (N and D).

Three vowels (I, I and A) can be arranged at odd position in \(\frac{3!}{2!} = 3 \) ways

2 consonants(N and D) can be arranged in 2! ways = 2 ways. 

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Thus, required numbers of ways = (3) (2) = 6.

∴ Option (b) is correct.

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